Tony Blair waded into the row over Tory plans to put a cap on tax relief for charities when he said the government should change its mind to avoid "a battle with the philanthropic sector that I think they will find it difficult to win".

The former prime minister said: "The best thing is to disentangle completely the idea of philanthropy and giving to charity from tax avoidance."

His remarks came as two opinion polls suggested the succession of post-budget rows, including over charitable tax relief, was starting to inflict serious damage on the coalition.

Blair, giving a long-planned speech on philanthropy in Washington, said: "It would be wise for them to think again. We should be doing everything we can at the moment to encourage the philanthropic sector. The third sector was a big part of our agenda when we were in government and I think it is still very important and in times of economic difficulty even more so.

"Anybody who is giving money to a charity if they are giving it to a genuine charitable cause they are losing money. If they are not giving it to a genuine charity, or the charity is not doing work with a proper public benefit, there is an armoury and battery of rules to make sure this did not happen.

"I am sure the government does not want intentionally to harm the philanthropic sector, and it would be daft to do so, and I am sure they don't want to do it, but sometimes things slip through and they are not right."

Blair warned David Cameron: "Don't end up in a situation where you imply people are donating for tax avoidance because I don't think that is the case."

The prime minister, now facing the eighth day of a backlash over plans to put a cap on tax relief, promised the government would listen sympathetically during a consultation this summer on the plans.

He said: "This was never going to be introduced until next year... there will be plenty of time to get it right, plenty of time to consult and to listen."

The controversies caused by the budget are starting to have a serious impact on the coalition parties. The regular YouGov/Sun tracker showed UKip third, ahead of the Liberal Democrats. The poll put Labour on 43%, Tories 32%, UKIP 9% and Lib Dems 8%. The Labour lead is their joint largest of the parliament.

A poll by Populus for the Times shows Labour on 42%, Conservatives 33%, Lib Dems 11% and others 16% – the highest Labour lead and the joint lowest Tory rating in this poll in this parliament.

The poll shows the shadow chancellor, Ed Balls, and the chancellor, George Osborne, are on level terms.

The polls come weeks before the 3 May local elections and London mayoral election, where Boris Johnson is still six points ahead of his rival, Ken Livingstone.

On BBC2's Newsnight, Blair warned the coalition that sometimes it appeared to be "a marriage of convenience rather marriage of conviction. The danger is that in that policy trade you can sometimes get incoherence. I would make sure before these polices are announced a little more in-depth policy work has been done".

On the same programme, Lady Warsi, the Conservative chairwoman, complained the budget had been poorly communicated because some of the big plans had been leaked in advance, leaving a focus on some issues such as the granny tax. She added: "When you are in coalition, it is not easy to have a very clear narrative and sometimes out of that comes some incoherence." She criticised the business secretary, Vince Cable, for his attacks on the budget: "If you agree something in cabinet, I think you stand by it."

The Treasury minister, David Gauke, said the plans to impose a cap on charitable tax relief might raise £50m-£100m,

Labour will on Wednesday seek a vote in parliament over the tax cap, with shadow chief secretary to the Treasury, Rachel Reeves, accusing the government of being in "a complete mess" over the issue.